# Condensed matter physics, area laws & LQG?

1. Aug 11, 2015

### atyy

http://arxiv.org/abs/1508.02538
Hessian geometry and entanglement thermodynamics
Hiroaki Matsueda
(Submitted on 11 Aug 2015)
We reconstruct
entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of entanglement thermodynamics, we derive that a proper choice of the Hessian potential leads to both of the entanglement entropy scaling for quantum critical systems and hyperbolic metric (or AdS space with imaginary time). We also derive geometric representation of the entanglement entropy in which the entropy is described as integration of local conserved current of information flowing across an entangling surface. We find that the entangling surface is equivalent to the domain boundary of the Hessian potential. This feature originates in a special property of critical systems in which we can identify the entanglement entropy with the Hessian potential after the second derivative by the canonical parameters, and this identification guarantees violation of extensive nature of the entropy.

2. Aug 26, 2015

### atyy

http://arxiv.org/abs/1508.06572
Quantum information erasure inside black holes
David A. Lowe, Larus Thorlacius
(Submitted on 26 Aug 2015)
An effective field theory for infalling observers in the vicinity of a quasi-static black hole is given in terms of a freely falling lattice discretization. The lattice model successfully reproduces the thermal spectrum of outgoing Hawking radiation, as was shown by Corley and Jacobson, but can also be used to model observations made by a typical low-energy observer who enters the black hole in free fall at a prescribed time. The explicit short distance cutoff ensures that, from the viewpoint of the infalling observer, any quantum information that entered the black hole more than a scrambling time earlier has been erased by the black hole singularity. This property, combined with the requirement that outside observers need at least of order the scrambling time to extract quantum information from the black hole, ensures that a typical infalling observer does not encounter drama upon crossing the black hole horizon in a theory where black hole information is preserved for asymptotic observers.

3. Sep 1, 2015

### marcus

http://arxiv.org/abs/1509.00113
Entanglement Holography
Jan de Boer, Michal P. Heller, Robert C. Myers, Yasha Neiman
(Submitted on 1 Sep 2015)
We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent time-like direction in dS is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS.
6 pages, 4 figures

http://arxiv.org/abs/1509.00074
A coarse-grained generalized second law for holographic conformal field theories
William Bunting, Zicao Fu, Donald Marolf
(Submitted on 31 Aug 2015)
We consider the universal sector of a d-dimensional large-N strongly-interacting holographic CFT on a black hole spacetime background B. When our CFTd is coupled to dynamical Einstein-Hilbert gravity with Newton constant Gd, the combined system can be shown to satisfy a version of the thermodynamic Generalized Second Law (GSL) at leading order in Gd. ...
17 pages, 1 figure

4. Sep 8, 2015

### atyy

http://arxiv.org/abs/1509.02036
A note on quantum supergravity and AdS/CFT
Norbert Bodendorfer
(Submitted on 7 Sep 2015)
We note that the non-perturbative quantisation of supergravity as recently investigated using loop quantum gravity techniques provides an opportunity to probe an interesting sector of the AdS/CFT correspondence, which is usually not considered in conventional treatments. In particular, assuming a certain amount of convergence between the quantum supergravity sector of string theory and quantum supergravity constructed via loop quantum gravity techniques, we argue that the large quantum number expansion in loop quantum supergravity corresponds to the $1/{N_{c}}^2$ expansion in the corresponding gauge theory. In order to argue that we are indeed dealing with an appropriate quantum supergravity sector of string theory, high energy ($α^{′}$) corrections are being neglected, leading to a gauge theory at strong coupling, yet finite $N_{c}$. The arguments given in this paper are mainly of qualitative nature, with the aim of serving as a starting point for a more in depth interaction between the string theory and loop quantum gravity communities.

5. Sep 8, 2015

### atyy

The latest paper by Norbert Bodendorfer http://arxiv.org/abs/1509.02036v1 referenced in post #304 says "The main purpose of this paper is to point out that using techniques from loop quantum gravity [10, 11, 12], a quantisation of supergravity has been constructed [13] which is a good candidate to describe string theory in the appropriate limit corresponding to a strongly coupled gauge theory with a finite number of colours."

Another paper about finite N is Brian Swingle and Mark Van Raamsdonk's http://arxiv.org/abs/1405.2933. Are they talking about the same thing?

6. Oct 9, 2015

### atyy

http://arxiv.org/abs/1510.02103
Holographic RG flows, entanglement entropy and the sum rule
Horacio Casini, Eduardo Teste, Gonzalo Torroba
(Submitted on 7 Oct 2015)
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d=2 and in d>2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.

http://arxiv.org/abs/1510.02367
Bulk Locality from Entanglement in Gauge/Gravity Duality
Jennifer Lin
(Submitted on 8 Oct 2015)
Gauge/gravity duality posits an equivalence between certain strongly coupled quantum field theories and theories of gravity with negative cosmological constant in a higher number of spacetime dimensions. The map between the degrees of freedom on the two sides is non-local and incompletely understood. I describe recent work towards characterizing this map using entanglement in the QFT, where near the dual AdS boundary, the classical energy density at a point in the bulk is stored in the relative entropies of boundary subregions whose homologous minimal surfaces pass through the bulk point. I also derive bulk classical energy conditions near the AdS boundary from entanglement inequalities in the CFT. This is based on the paper [1] with Matilde Marcolli, Hirosi Ooguri and Bogdan Stoica.
More generally, in recent years, there has appeared some evidence that quantum entanglement is responsible for the emergence of spacetime. I review and comment on the state of these developments.

7. Oct 15, 2015

### atyy

http://arxiv.org/abs/1510.04492
An Introduction to Emergent Symmetries
Pedro R. S. Gomes
(Submitted on 15 Oct 2015)
These are intended to be introductory notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some elementary background material and proceed to our discussion by examining several interesting problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.

8. Oct 27, 2015

### atyy

http://quantumfrontiers.com/2015/08/16/quantum-information-meets-quantum-matter/
Blog post by Xie Chen: Quantum Information meets Quantum Matter

http://arxiv.org/abs/1508.02595
Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems

Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
(Submitted on 11 Aug 2015 (v1), last revised 21 Sep 2015 (this version, v2))
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

Comments: Hyperref added. This draft is by no means final. Substantial scientific and format changes are still to be made. We have received many helpful comments. We are very grateful for them and will incorporate them into later versions. Please keep sending us comments. The full edition of the book will be available from Springer, in which we will acknowledge the help we have received from everyone

9. Oct 27, 2015

### marcus

335 pages, many figures. check out the table of contents. Doesn't have an alphabetized index yet---something that will make it much easier to use in future.
Wide innovative encompassing vision---XG Wen style. Could become influential. Thanks for spotting this!

10. Nov 3, 2015

### democrito

http://arxiv.org/abs/1510.09020
Entanglement Renormalization and Two Dimensional String Theory
Javier Molina-Vilaplana

The entanglement renormalization flow of a (1+1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.

11. Nov 11, 2015

### atyy

12. Nov 13, 2015

### serp777

Well, to be honest, nothing about entanglement is "intuitive" in my opinion, but maybe its more understandable for people with a physics degree.

13. Nov 19, 2015

### atyy

14. Dec 9, 2015

### atyy

http://arxiv.org/abs/1512.02695
Speed Limits for Entanglement
Thomas Hartman, Nima Afkhami-Jeddi
(Submitted on 8 Dec 2015)
We show that in any relativistic system, entanglement entropy obeys a speed limit set by the entanglement in thermal equilibrium. The bound is derived from inequalities on relative entropy with respect to a thermal reference state. Thus the thermal state constrains far-from-equilibrium entanglement dynamics whether or not the system actually equilibrates, in a manner reminiscent of fluctuation theorems in classical statistical mechanics. A similar shape-dependent bound constrains the full nonlinear time evolution, supporting a simple physical picture for entanglement propagation that has previously been motivated by holographic calculations in conformal field theory. We discuss general quantum field theories in any spacetime dimension, but also derive some results of independent interest for thermal relative entropy in 1+1d CFT.

15. Dec 11, 2015

### atyy

http://arxiv.org/abs/1512.03388
Quantum entanglement in condensed matter systems
Nicolas Laflorencie
(Submitted on 10 Dec 2015)
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated R\'enyi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in details. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.

16. Dec 13, 2015

### atyy

.Scott started a discussion on an extremely interesting paper in https://www.physicsforums.com/threads/spectral-gap-or-gapless-undecidable.847554/

http://arxiv.org/abs/1502.04135
Undecidability of the Spectral Gap (short version)
Toby Cubitt, David Perez-Garcia, Michael M. Wolf
(Submitted on 13 Feb 2015)
The spectral gap -- the difference in energy between the ground state and the first excited state -- is one of the most important properties of a quantum many-body system. Quantum phase transitions occur when the spectral gap vanishes and the system becomes critical. Much of physics is concerned with understanding the phase diagrams of quantum systems, and some of the most challenging and long-standing open problems in theoretical physics concern the spectral gap, such as the Haldane conjecture that the Heisenberg chain is gapped for integer spin, proving existence of a gapped topological spin liquid phase, or the Yang-Mills gap conjecture (one of the Millennium Prize problems). These problems are all particular cases of the general spectral gap problem: Given a quantum many-body Hamiltonian, is the system it describes gapped or gapless?
Here we show that this problem is undecidable, in the same sense as the Halting Problem was proven to be undecidable by Turing. A consequence of this is that the spectral gap of certain quantum many-body Hamiltonians is not determined by the axioms of mathematics, much as Goedels incompleteness theorem implies that certain theorems are mathematically unprovable. We extend these results to prove undecidability of other low temperature properties, such as correlation functions. The proof hinges on simple quantum many-body models that exhibit highly unusual physics in the thermodynamic limit.

Comments: 8 pages, 3 figures. See long companion paper arXiv:1502.04573 (same title and authors) for full technical details

17. Dec 16, 2015

### marcus

http://arxiv.org/abs/1512.04993
Complexity, Action, and Black Holes
Adam Brown, Daniel A. Roberts, Leonard Susskind, Brian Swingle, Ying Zhao
(Submitted on 15 Dec 2015)
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the `Wheeler-DeWitt' patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are fastest computers in nature.

18. Dec 21, 2015

### atyy

http://arxiv.org/abs/1512.06206
Finite Entanglement Entropy of Black Holes
Stefano Giaccari, Leonardo Modesto, Leslaw Rachwal, Yiwei Zhu
(Submitted on 19 Dec 2015)
We compute the area term contribution to the black holes' entanglement entropy for a class of local or weakly nonlocal renormalizable gravitational theories coupled to matter. For the case of super-renormalizable theories, we can get a finite conical entropy expressed only in terms of the classical Newton constant either by completing the theory to a finite one in dimensional regularization or by removing the quadratic divergences in the cut-off regularization by the introduction of additional interaction terms. Therefore, our result is independent from the renormalization scheme. We also propose a theory in which the renormalization of the Newton constant is entirely due to the standard model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.

http://arxiv.org/abs/1512.06431
Relative entropy equals bulk relative entropy
Daniel L. Jafferis, Aitor Lewkowycz, Juan Maldacena, S. Josephine Suh
(Submitted on 20 Dec 2015)
We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

http://arxiv.org/abs/1512.06784
The 1/N expansion method in quantum field theory
H. Sazdjian
(Submitted on 16 Dec 2015)
The motivations of the 1/N expansion method in quantum field theory are explained. The method is first illustrated with the O(N) model of scalar fields. A second example is considered with the two-dimensional Gross-Neveu model of fermion fields with global U(N) and discrete chiral symmetries. The case of QCD is briefly sketched.

19. Jan 22, 2016

### atyy

http://arxiv.org/abs/1601.05416
Bulk Reconstruction in the Entanglement Wedge in AdS/CFT
Xi Dong, Daniel Harlow, Aron C. Wall
(Submitted on 20 Jan 2016)
In this note we prove a simple theorem in quantum information theory, which implies that bulk operators in the Anti-de Sitter / Conformal Field Theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A, provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.

http://arxiv.org/abs/1601.05611
Asymmetric interiors for small black holes
(Submitted on 21 Jan 2016)
We develop the representation of infalling observers and bulk fields in the CFT as a way to understand the black hole interior in AdS. We first discuss properties of CFT states which are dual to black holes. Then we show that in the presence of a Killing horizon bulk fields can be decomposed into pieces we call ingoing and outgoing. The ingoing field admits a simple operator representation in the CFT, even inside a small black hole at late times, which leads to a simple CFT description of infalling geodesics. This means classical infalling observers will experience the classical geometry in the interior. The outgoing piece of the field is more subtle. In an eternal two-sided geometry it can be represented as an operator on the left CFT. In a stable one-sided geometry it can be described using entanglement via the PR construction. But in an evaporating black hole trans-horizon entanglement changes at the Page time, which means that for old black holes the PR construction fails and the outgoing field does not see local geometry. This picture of the interior allows the CFT to reconcile unitary Hawking evaporation with the classical experience of infalling observers.

20. Jan 24, 2016

### marcus

http://arxiv.org/abs/1601.05707
Projective quantum states for Loop Quantum Gravity coupled to tensor fields
Andrzej Okolow
(Submitted on 21 Jan 2016)
We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity obtained by Lanery and Thiemann we construct quantum states for LQG coupled to tensor fields.
23 pages.
[Atyy, please let me know if this paper does not fit comfortably in your bibliography and I'll delete it]